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A current of 15A flows through a coil Ma...

A current of 15A flows through a coil Magnetic field at centre of semi-circular loop of 5.0 cm radius as shown in fig. Find out the direction and magnitude of magnetic field at the centre of the arc.

Text Solution

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`I = 15 a`
`a = 5.0 cm`
`a = 5 xx 10^(-2) m`
`(mu_0)/(4pi) = 10^(-7) T mA^(-1)`

Magnetic field at the centre of circular loop
`= (mu_0)/(4pi) (2 pi I)/(a)`
Magnetic field at centre of semi-circular loop
`= 1/2 xx (mu_0)/(4pi) (2 pi I)/a`
`= 1/2 xx 10^(-7) xx 2 xx 22/7 xx 15/(5 xx 10^(-2))`
`= 9.42 xx 10^(-5) T`
Magnetic field will be normal to plane of paper but in upward direction.
Magnetic field at the centre of currect carrying arc due to straight portion i.e., due to AB and CD is zero. So at centre , net magnetic field = `9.42 xx 10^(-5) + 0 = 9.42 xx 10^(-5) T`.
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